Problem: Simplify the following expression: $z = \dfrac{k}{6} - \dfrac{k}{7}$
Explanation: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $6$ and $7$ $\lcm(6, 7) = 42$ $ z = \dfrac{7}{7} \cdot \dfrac{k}{6} - \dfrac{6}{6} \cdot \dfrac{k}{7} $ $z = \dfrac{7k}{42} - \dfrac{6k}{42}$ $z = \dfrac{7k -6k}{42}$ $z = \dfrac{k}{42}$